M. Doostparast, M. Hashempour, 1. E.VelayatiMoghaddam
In engineering systems, it is usually assumed that lifetimes of components are independent and identically distributed (iid). But, the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components change. For modeling this kind of systems, the theory of sequential order statistics (SOS) can be used. Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory, the maximum likelihood estimates of the unknown parameters are obtained in different cases. A new model, denoted by PTCPHM, as a generalization of the iid case is proposed, and then statistical inferential methods including point and interval estimation as well as hypothesis tests under PTCPHM are then developed. Finally, a real data on failure times of aircraft components, due to Mann and Fertig (1973), is analyzed to illustrate the model and inferential methods developed here.
{"title":"Weibull Analysis with Sequential Order Statistics Under a Power Trend Model for Hazard Rates with Application in Aircraft Data Analysis","authors":"M. Doostparast, M. Hashempour, 1. E.VelayatiMoghaddam","doi":"10.52547/jsri.16.2.535","DOIUrl":"https://doi.org/10.52547/jsri.16.2.535","url":null,"abstract":"In engineering systems, it is usually assumed that lifetimes of components are independent and identically distributed (iid). But, the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components change. For modeling this kind of systems, the theory of sequential order statistics (SOS) can be used. Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory, the maximum likelihood estimates of the unknown parameters are obtained in different cases. A new model, denoted by PTCPHM, as a generalization of the iid case is proposed, and then statistical inferential methods including point and interval estimation as well as hypothesis tests under PTCPHM are then developed. Finally, a real data on failure times of aircraft components, due to Mann and Fertig (1973), is analyzed to illustrate the model and inferential methods developed here.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115697190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A New Lifetime Distribution: The Beta Modified Weibull Power Series Distribution","authors":"E. Bahrami, Narges Yarmoghaddam","doi":"10.52547/jsri.16.1.1","DOIUrl":"https://doi.org/10.52547/jsri.16.1.1","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131188801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation of Reliability of Stress-strength for a Kumaraswamy Distribution based on Progressively Censored Sample","authors":"A. Kohansal, R. Kazemi","doi":"10.52547/jsri.16.1.165","DOIUrl":"https://doi.org/10.52547/jsri.16.1.165","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132780602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Repetitive Sampling-based Control Chart for Multivariate Weighed Poisson Distribution with Two Different Indexes","authors":"S. Enami, H. Torabi","doi":"10.52547/jsri.16.1.245","DOIUrl":"https://doi.org/10.52547/jsri.16.1.245","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131213601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spatial Statistics Analysis to Identify Hot Spots Using Accidental Event Calls Services","authors":"Samira Ghashghaie, S. Behzadi","doi":"10.52547/jsri.16.1.121","DOIUrl":"https://doi.org/10.52547/jsri.16.1.121","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123004692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this article, we study parameter estimation of the logarith mic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown pa rameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parame ter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numeri cal results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An exam ple via a real dataset is presented for the illustrative purposes.
{"title":"Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations","authors":"Mahdi Rasekhi, Gholamhossein G. Hamedani","doi":"10.52547/jsri.16.1.59","DOIUrl":"https://doi.org/10.52547/jsri.16.1.59","url":null,"abstract":". In this article, we study parameter estimation of the logarith mic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown pa rameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parame ter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numeri cal results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An exam ple via a real dataset is presented for the illustrative purposes.","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124358479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Results on Stochastic Comparison of Series and Parallel Systems Comprising Heterogeneous Generalized Modified Weibull Components","authors":"Esmaeil Bashkar","doi":"10.52547/jsri.16.1.101","DOIUrl":"https://doi.org/10.52547/jsri.16.1.101","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129009748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ahangari, M. Golalizadeh, Zahra Rezaei Ghahroodi
{"title":"Likelihood Inference in the Random Effects Logistic Regression Model with Response Misclassification and Covariate Subject to Measurement Error","authors":"M. Ahangari, M. Golalizadeh, Zahra Rezaei Ghahroodi","doi":"10.52547/jsri.16.1.255","DOIUrl":"https://doi.org/10.52547/jsri.16.1.255","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"303 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117210780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comparison of Record Ranked Set Sampling and Ordinary Records in Prediction of Future Record Statistics from an Exponential Distribution","authors":"Ehsan Golzade Gervi, P. Nasiri, M. Salehi","doi":"10.52547/jsri.16.1.73","DOIUrl":"https://doi.org/10.52547/jsri.16.1.73","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131068883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Dynamic Survival Past Extropy Properties","authors":"Zohreh Pakdaman, Majid Hashempour","doi":"10.52547/jsri.16.1.229","DOIUrl":"https://doi.org/10.52547/jsri.16.1.229","url":null,"abstract":"","PeriodicalId":422124,"journal":{"name":"Journal of Statistical Research of Iran","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122176038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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